Abstract: In order to improve the ability of a company to deal with emergent events and a capital reorganization, based on the default capital reorganization scheme of debt-equity swap, we investigate the pricing problem of the perpetual corporate debt and the optimal capital structure under the framework of a jump-diffusion model with $-1$ jump size. Problems are solved by applying the optimal stopping technique and a structural method. The closed-form formulas for the perpetual corporate debt, the equity and the total value of corporate are obtained by a differential equation method, moreover, the optimal default boundary and the optimal leverage ratio are also given. Finally, a numerical analysis is conducted to reveal the financial phenomenon caused by the jump intensity.

Key words: structural method, jump-diffusion, default capital reorganization, perpetual corporate debt, optimal leverage ratio